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Two-Stage Procedures for High-Dimensional Data
http://hdl.handle.net/2241/117753
http://hdl.handle.net/2241/1177535ba6ba36-6bc4-4c3f-bc30-2808d98874cc
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SA_30-4-432.pdf (96.7 kB)
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SA_30-4-356.pdf (1.1 MB)
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Item type | Journal Article(1) | |||||
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公開日 | 2012-11-07 | |||||
タイトル | ||||||
タイトル | Two-Stage Procedures for High-Dimensional Data | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | Asymptotic normality | |||||
キーワード | ||||||
主題 | Classification | |||||
キーワード | ||||||
主題 | Confidence region | |||||
キーワード | ||||||
主題 | HDLSS | |||||
キーワード | ||||||
主題 | Lasso | |||||
キーワード | ||||||
主題 | Pathway analysis | |||||
キーワード | ||||||
主題 | Regression | |||||
キーワード | ||||||
主題 | Sample size determination | |||||
キーワード | ||||||
主題 | Testing equality of covariance matrices | |||||
キーワード | ||||||
主題 | Two-sample test | |||||
キーワード | ||||||
主題 | Variable selection | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Aoshima, Makoto
× Aoshima, Makoto× Yata, Kazuyoshi |
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著者別名 |
青嶋, 誠
× 青嶋, 誠× 矢田, 和善 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In this article, we consider a variety of inference problems for high-dimensional data. The purpose of this article is to suggest directions for future research and possible solutions about p n problems by using new types of two-stage estimation methodologies. This is the first attempt to apply sequential analysis to high-dimensional statistical inference ensuring prespecified accuracy. We offer the sample size determination for inference problems by creating new types of multivariate two-stage procedures. To develop theory and methodologies, the most important and basic idea is the asymptotic normality when p → ∞. By developing asymptotic normality when p → ∞, we first give (a) a given-bandwidth confidence region for the square loss. In addition, we give (b) a two-sample test to assure prespecified size and power simultaneously together with (c) an equality-test procedure for two covariance matrices. We also give (d) a two-stage discriminant procedure that controls misclassification rates being no more than a prespecified value. Moreover, we propose (e) a two-stage variable selection procedure that provides screening of variables in the first stage and selects a significant set of associated variables from among a set of candidate variables in the second stage. Following the variable selection procedure, we consider (f) variable selection for high-dimensional regression to compare favorably with the lasso in terms of the assurance of accuracy and the computational cost. Further, we consider variable selection for classification and propose (g) a two-stage discriminant procedure after screening some variables. Finally, we consider (h) pathway analysis for high-dimensional data by constructing a multiple test of correlation coefficients. | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Editor's Special Invited Paper。 この招待論文は、Abraham Wald Prize in Sequential Analysis 2012の受賞論文となっております。 |
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書誌情報 |
Sequential analysis 巻 30, 号 4, p. 356-399, 発行日 2011-11 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0747-4946 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA10538981 | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.1080/07474946.2011.619088 | |||||
権利 | ||||||
権利情報 | © Taylor & Francis Group, LLC. This is an Author's Accepted Manuscript of an article published in Sequential Analysis Nov 2011 , available online at: http://www.tandfonline.com/doi/full/10.1080/07474946.2011.619088 |
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著者版フラグ | ||||||
値 | author | |||||
出版者 | ||||||
出版者 | Taylor & Francis | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2241/117753 | |||||
識別子タイプ | HDL | |||||
関係URI | ||||||
関連名称 | http://hdl.handle.net/2241/117756 |